what is a vocal processor?

Other than the preamp (you wrote). Preamps are a different thing, not what I would call a processor.
A vocal processor is kind of like a guitar effects processor, but made just for vocals. They do all of those things that you stated. You can get a cheap decent sounding delay, chorus, auto pitch correct, (and whaever else) in a vocal processing unit for faily cheap. But when you are trying to harmonize the cheap stuff sounds bad, real bad.

The term "voice processor" means different things to different people. Amost ANY of the ones I've seen or owned did have a mic pre in them.
They also provide dynamics control of some sort-typically compression, de-essing, and perhaps a downward expander and/or a gate. Perhaps EQ designed to center on the human voice range. Analog units like the dbx 286, the Drawmer Front End One, the Valley People Air Force One, all fit that bill. Even the digital models, such as the Antares, the dbx Pro Vocal, and the TC Helicon have a mic pre, and many of the previously-mentioned features. They might also include DSP-based effects like pitch-correction/changing, delay, and mic modeling and reverb algorithms.
The reason that they are referred to as "voice processors" is because the parameters of the functions (dynamics, EQ, etc) are "tuned to" the anomalies of the human voice. But that doesn't relegate them to just that. I've used them to control noisey Marshalls, squeaky Martins, cymbal-slashers, and the like. A variation of these is often called a "channel strip".